Very hush-hush (3-6)
I believe the answer is:
top-secret
'very hush-hush' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for top-secret that I've seen before include "Highly classified" , "(Of information) strictly not for public consumption" , "Of the highest security classification" , "Highly restricted (information)" , "Highest classified (information)" .)